some way for the npc to chase a player who attacks him from a long distance with the bow, the npc in question is melee

If I understand you correctly, you want to be able to attack the NPC from a long distance, but the NPC doesn't fight back because the Agro Range is too small. But you also don't want to set the agro range so high because the NPC will then attack you from a long distance.
I would try scripting:
When the NPC is attacked, set the Agro Range to maximum. Then he shouldn't see you before your attack, but after.
I'm currently trying to solve a problem like this myself, and if I get it right, I'll share it with you